How can I rearrange the domino tiles below so that all vertical columns has 0,1,2,3,4,5,6. While all the horizontal rows has 0,1,2,3,4,5,6 + duplicate ?
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$\begingroup$ I'm not sure, what do you mean with "+duplicate"? Could you clarify the question? $\endgroup$– AlenannoOct 19, 2016 at 19:42
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$\begingroup$ Disclaimer: I don't know how $\endgroup$– TSLFOct 19, 2016 at 19:44
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$\begingroup$ @TSLF if this isn't your puzzle you need to credit the source otherwise it is plagiarism $\endgroup$– Beastly GerbilOct 19, 2016 at 19:44
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$\begingroup$ I managed to do all vertical but I am not sure if this is possible. $\endgroup$– TSLFOct 19, 2016 at 19:59
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1$\begingroup$ By duplicate do you mean you can have one duplicate value. For example row 1 will contain (0,1), (2,3), (4,5),(6,4) where 4 is a duplicate or (0,1), (2,3), (4,5),(6,6) where 6 is a tile with the same value on both sides. And are you supposed to have 2 (5,6) tiles or should the last one be (6,6) $\endgroup$– gtwebbOct 19, 2016 at 20:15
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1 Answer
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As noted in the comments to the question, the tiles in the picture form a standard set except for an extra 5/6 and a missing 6/6. If we assume the picture to be correct,
It's impossible, as there aren't enough sixes to cover all 8 columns.
Otherwise, making the assumption that we are supposed to arrange a standard set:
Any double already creates a duplicate, so we have to have one double in each row. Therefore, I started by placing all doubles in the first column. To keep the pattern going, I arranged all tiles with a difference of 1 or 6 in the second column, differences of 2 or 5 went in the third column, and finally 3 or 4 in the fourth column:
00 23 46 51 11 34 50 62 22 45 61 03 33 56 02 14 44 60 13 25 55 01 24 36 66 12 35 40
